In this course, we will cover few classical
LP topics, including Simplex-Method, Duality and Decomposition. Our main
concentration, however, will be on recent developments in the IPM, including
the original affine scaling method by I.I.Dikin (1967) and projective scaling
algorithm by N.Karmarker (1984).

We will discuss the path-following central
path and primal-dual IPM's, which are based on Classical Barrier and Distance
functions. We will cover the basic results of the Modified Barrier Functions
(MBF) theory for LP. Complexity issues, as well as numerical realizations,
of the IPMs will be discussed.

We will have a computational project, which
requires using CPLEX software.